Simplify (-(2x^(1/6))/(3y^4))^-3

${(- \frac{2 x^{\frac{1}{6}}}{3 y^{4}})}^{- 3}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- \frac{3 y^{4}}{2 x^{\frac{1}{6}}})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{3 y^{4}}{2 x^{\frac{1}{6}}}$ .

${(- 1)}^{3} {(\frac{3 y^{4}}{2 x^{\frac{1}{6}}})}^{3}$

Apply the product rule to $\frac{3 y^{4}}{2 x^{\frac{1}{6}}}$ .

${(- 1)}^{3} \frac{{(3 y^{4})}^{3}}{{(2 x^{\frac{1}{6}})}^{3}}$

Apply the product rule to $3 y^{4}$ .

${(- 1)}^{3} \frac{3^{3} {(y^{4})}^{3}}{{(2 x^{\frac{1}{6}})}^{3}}$

Apply the product rule to $2 x^{\frac{1}{6}}$ .

${(- 1)}^{3} \frac{3^{3} {(y^{4})}^{3}}{2^{3} {(x^{\frac{1}{6}})}^{3}}$

Raise $- 1$ to the power of $3$ .

$- \frac{3^{3} {(y^{4})}^{3}}{2^{3} {(x^{\frac{1}{6}})}^{3}}$

Simplify the numerator.

Raise $3$ to the power of $3$ .

$- \frac{27 {(y^{4})}^{3}}{2^{3} {(x^{\frac{1}{6}})}^{3}}$

Multiply the exponents in ${(y^{4})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{27 y^{4 \cdot 3}}{2^{3} {(x^{\frac{1}{6}})}^{3}}$

Multiply $4$ by $3$ .

$- \frac{27 y^{12}}{2^{3} {(x^{\frac{1}{6}})}^{3}}$

Simplify the denominator.

Raise $2$ to the power of $3$ .

$- \frac{27 y^{12}}{8 {(x^{\frac{1}{6}})}^{3}}$

Multiply the exponents in ${(x^{\frac{1}{6}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{27 y^{12}}{8 x^{\frac{1}{6} \cdot 3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$- \frac{27 y^{12}}{8 x^{\frac{1}{3 (2)} \cdot 3}}$

Cancel the common factor.

$- \frac{27 y^{12}}{8 x^{\frac{1}{3 \cdot 2} \cdot 3}}$

Rewrite the expression.

$- \frac{27 y^{12}}{8 x^{\frac{1}{2}}}$